Neurodegenerative damage reduces firing coherence in a continuous attractor model of grid cells

Grid cells in the dorsolateral band of the medial entorhinal cortex (dMEC) display strikingly regular periodic firing patterns on a lattice of positions in two-dimensional (2D) space. This helps animals to encode relative spatial location without reference to external cues. The dMEC is damaged in the early stages of Alzheimer's disease, which affects navigation ability of a disease victim, reducing the synaptic density of neurons in the network. Within an established two-dimensional continuous attractor neural network model of grid cell activity, we introduce neural sheet damage parametrized by radius and by the strength of the synaptic output for neurons in the damaged region. The mean proportionality of the grid field flow rate in the dMEC to the velocity of the model animal is maintained, but there is a broadened distribution of flow rates in the damaged case. This flow-rate-to-velocity proportionality is essential to establish coherent grid firing fields for individual grid cells for a roaming animal. When we examine the coherence of the grid cell firing field by studying Bragg peaks of the Fourier transformed lattice firing field intensity in both damaged and undamaged regions, we find that, for a wide range of damage radius and reduced synaptic strength, for undamaged model grid cells there is an incoherent firing field structure with only a single central peak. In the radius-damage plane this is adjacent to narrow bands of striped lattices (two additional Bragg peaks), which abut an orthorhombic pattern (four additional Bragg peaks), that abuts the undamaged hexagonal region (six additional Bragg peaks). Within the damaged region, grid cells show no Bragg peaks outside the central one, which shows reduced intensity with increasing damage, and outside the damaged region the central Bragg peak strength is largely unaffected. There is a reentrant region of normal grid firing fields for very large damage area. We anticipate that the modified grid cell behavior can be observed in noninvasive functional magnetic resonance imaging (fMRI) of the dMEC.